Question: Simplify the following expression: $z = \dfrac{4y}{9} + \dfrac{y}{10}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $9$ and $10$ $\lcm(9, 10) = 90$ $ z = \dfrac{10}{10} \cdot \dfrac{4y}{9} + \dfrac{9}{9} \cdot \dfrac{y}{10} $ $z = \dfrac{40y}{90} + \dfrac{9y}{90}$ $z = \dfrac{40y +9y}{90}$ $z = \dfrac{49y}{90}$